Find the ratio of gravitational potential energy if height of an object is doubled
and mass is tripled. Also find ratio of work done by gravity in bringing the
object to zero height in both cases
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Answer:
Ratio of potential energy,
Potential energy in the 1st case,
Ep = mgh
Ep = mg2h ………….if height is doubled ………. (1)
Potential energy in the 2nd case,
Ep = mgh
Ep = mg3h ………...if the height is tripled ……… (2)
From (1) and (2)
Ratio of their potential energy,
= mg2h / mg3h
= 2mgh / 3mgh
= 2/3
Therefore the ratio = 2 : 3
Now,
Ratio of work done,
Work done in the 1st case,
W = fs
W = f * 2s ……..since the distance was doubled
……….. (1)
W = 2fs
Work done in the 2nd case,
W = fs
W = f * 3s………..since the distance is tripled
………….. (2)
W = 3fs
From (1) and (2)
Ratio of their work done,
= 2fs / 3fs
= 2 / 3
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